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Parameter Analysis for Guarding Terrains

Akanksha Agrawal, Sudeshna Kolay, Meirav Zehavi, Susanne Albers
2020 Scandinavian Workshop on Algorithm Theory  
The Terrain Guarding problem is a well-known variant of the famous Art Gallery problem.  ...  In this paper, we focus on the parameterized complexity of Terrain Guarding (both discrete and continuous) with respect to two natural parameters.  ...  In particular, it is the most well-studied visibility problem except for the classic Art Gallery problem.  ... 
doi:10.4230/lipics.swat.2020.4 dblp:conf/swat/AgrawalKZ20 fatcat:7ushypru55d7nfwfdkjz3kb4eq

Topological Art in Simple Galleries [article]

Daniel Bertschinger, Nicolas El Maalouly, Tillmann Miltzow, Patrick Schnider, Simon Weber
2021 arXiv   pre-print
Let P be a simple polygon, then the art gallery problem is looking for a minimum set of points (guards) that can see every point in P.  ...  We denote by V(P) the family of all minimum guard placements. The Hausdorff distance makes V(P) a metric space and thus a topological space.  ...  [5] Akanksha Agrawal and Meirav Zehavi. Parameterized analysis of art gallery and terrain guarding. In International Computer Science Symposium in Russia, pages 16–29. Springer, 2020.  ... 
arXiv:2108.04007v1 fatcat:qifivyhmgrbzrn4fridq2iw2aq

Face-Guarding Polyhedra [article]

Giovanni Viglietta
2014 arXiv   pre-print
We study the Art Gallery Problem for face guards in polyhedral environments.  ...  Additionally, for closed face guards in 2-reflex orthostacks, we give a lower bound of (f+3)/9 and an upper bound of (f+1)/7.  ...  Acknowledgments The author wishes to thank the anonymous reviewers for precious suggestions on how to improve the readability of this paper.  ... 
arXiv:1305.2866v4 fatcat:ihb7recnfnd7lgnrhppaqo3tdy

Parameterized Hardness of Art Gallery Problems

Édouard Bonnet, Tillmann Miltzow
2020 ACM Transactions on Algorithms  
The Vertex Guard Art Gallery problem asks for 4 such a set S subset of the vertices of P. A point in the set S is referred to as a guard.  ...  of algorithms → Parameterized complexity and exact algorithms. 10  ...  The authors present an FPT algorithm for Vertex Guard Art Gallery under this 94 parameterization. See also [4] for FPT algorithms on the (strong) conflict-free coloring of terrains.  ... 
doi:10.1145/3398684 fatcat:25gzjq2u2bbkhi3pte4wqj5awy

Irrational Guards are Sometimes Needed [article]

Mikkel Abrahamsen, Anna Adamaszek, Tillmann Miltzow
2017 arXiv   pre-print
In this paper we study the art gallery problem, which is one of the fundamental problems in computational geometry.  ...  Despite an extensive study of the art gallery problem, it remained an open question whether there are polygons given by integer coordinates that require guard positions with irrational coordinates in any  ...  Tillmann Miltzow is supported by the ERC grant "PARAMTIGHT: Parameterized complexity and the search for tight complexity results", no. 280152.  ... 
arXiv:1701.05475v1 fatcat:27pzk2btyna6phasgipnpwjkmq

Efficient 3D region guarding for multimedia data processing

Wuyi Yu, Maoqing Li, S. S. Iyengar, Xin Li
2011 2011 IEEE International Conference on Multimedia and Expo  
We show the effectiveness of our algorithm and briefly illustrate its applications in multimedia data processing and computer graphics such as shape analysis and retrieval, and morphing animation.  ...  Their effective analysis, integration, and retrieval are important research topics in multimedia. This paper studies a geometric modeling problem called 3D region guarding.  ...  The gallery guarding problem has been studied in computational geometry community on 2D planar domains and in 2.5D for terrain guarding.  ... 
doi:10.1109/icme.2011.6011953 dblp:conf/icmcs/YuLIL11 fatcat:x562qudxkfcqzjlqvesky5gc4q

Sweeping a terrain by collaborative aerial vehicles

Alon Efrat, Mikko Nikkilä, Valentin Polishchuk
2013 Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems - SIGSPATIAL'13  
We give algorithms for motion planning and coordination for a team of UAVs under various assumptions on the vehicles equipage/capabilities and present outputs of an implementation of the algorithms.  ...  Mountainous regions are typically hard to access by land; because of this, search operations in hilly terrains are often performed by airborne force such as Unmanned Aerial Vehicles (UAVs).  ...  Placing static guards to see a polygonal domain is the famous Art Gallery Problem [20] ; finding a route for a single guard that sees a domain is the subject in the Watchman Route Problem [17, 10] (  ... 
doi:10.1145/2525314.2525355 dblp:conf/gis/EfratNP13 fatcat:rvj7m3y2ufc3lobsviieyeipk4

Approximate Guarding of Monotone and Rectilinear Polygons [chapter]

Bengt J. Nilsson
2005 Lecture Notes in Computer Science  
Computational geometry Art gallery problems Monotone polygons Rectilinear polygons Approximation algorithms  ...  We show that vertex guarding a monotone polygon is NP-hard and construct a constant factor approximation algorithm for interior guarding monotone polygons.  ...  Art gallery problems are motivated by applications such as line-of-sight transmission networks in terrains, such as, signal communications and broadcasting, cellular telephony systems and other telecommunication  ... 
doi:10.1007/11523468_110 fatcat:h325z44x6bdhhfv4d52t7rumpu

Approximate Guarding of Monotone and Rectilinear Polygons

Erik A. Krohn, Bengt J. Nilsson
2012 Algorithmica  
Computational geometry Art gallery problems Monotone polygons Rectilinear polygons Approximation algorithms  ...  We show that vertex guarding a monotone polygon is NP-hard and construct a constant factor approximation algorithm for interior guarding monotone polygons.  ...  Art gallery problems are motivated by applications such as line-of-sight transmission networks in terrains, such as, signal communications and broadcasting, cellular telephony systems and other telecommunication  ... 
doi:10.1007/s00453-012-9653-3 fatcat:qpeezcrrabgwlenk3jovnrvgry

Optimal Camera Placement for Automated Surveillance Tasks

Robert Bodor, Andrew Drenner, Paul Schrater, Nikolaos Papanikolopoulos
2007 Journal of Intelligent and Robotic Systems  
As a result, this method differs significantly in its core formulation from camera placement solutions applied to problems such as inspection, reconstruction or the Art Gallery class of problems.  ...  an all terrain robot vehicle-Jr robot in an indoor setting.  ...  Institute at the University of Minnesota, and an NSF Graduate Research Fellowship.  ... 
doi:10.1007/s10846-007-9164-7 fatcat:nabxwrt4azcu5cd5zvjwpjlsl4

Optimal patrolling of fragmented boundaries

Andrew Collins, Jurek Czyzowicz, Leszek Gasieniec, Adrian Kosowski, Evangelos Kranakis, Danny Krizanc, Russell Martin, Oscar Morales Ponce
2013 Proceedings of the 25th ACM symposium on Parallelism in algorithms and architectures - SPAA '13  
These two fundamental types of strategies were studied in the past in the robotics community in different theoretical and experimental settings.  ...  A set of mobile robots is deployed on a simple curve of finite length, composed of a finite set of vital segments separated by neutral segments.  ...  Hence at one extremity, we obtain the case when m is large enough to have S = 0 (m stationary guards for art gallery are sufficient) and on the other extremity the single watchman question arises.  ... 
doi:10.1145/2486159.2486176 dblp:conf/spaa/CollinsCGKKKMP13 fatcat:ijqaqcelfzb7da63yh62dpzlku

Advancing Through Terrains [article]

Vincent Froese, Malte Renken
2020 arXiv   pre-print
Over the last decade, terrain visibility graphs attracted attention in the context of time series analysis with various practical applications in areas such as physics, geography and medical sciences.  ...  We devise a fast output-sensitive shortest path algorithm on terrain-like graphs and a polynomial-time algorithm for Dominating Set on special terrain visibility graphs (called funnel visibility graphs  ...  Dominating Set on Funnel Visibility Graphs In this section we consider the Dominating Set problem (which is a variant of the Art Gallery or Guarding problem in the context of visibility graphs) on a subclass  ... 
arXiv:1904.08746v3 fatcat:rxiwskt2j5fafoqa5mqv45xvq4

On Realistic Target Coverage by Autonomous Drones

Ahmed Saeed, Ahmed Abdelkader, Mouhyemen Khan, Azin Neishaboori, Khaled A. Harras, Amr Mohamed
2019 ACM transactions on sensor networks  
To achieve the full potential of such drones, it is necessary to develop new enhanced formulations of both common and emerging sensing scenarios.  ...  Low-cost mini-drones with advanced sensing and maneuverability enable a new class of intelligent sensing systems.  ...  Art Gallery Problem.  ... 
doi:10.1145/3325512 fatcat:ml2z6zs755gpjegulx7mceg6b4

On Realistic Target Coverage by Autonomous Drones [article]

Ahmed Saeed, Ahmed Abdelkader, Mouhyemen Khan, Azin Neishaboori, Khaled A. Harras, Amr Mohamed
2018 arXiv   pre-print
To achieve the full potential of such drones, it is necessary to develop new enhanced formulations of both common and emerging sensing scenarios.  ...  Low-cost mini-drones with advanced sensing and maneuverability enable a new class of intelligent sensing systems.  ...  Art Gallery Problem: A classical problem in discrete and computational geometry asks for the minimum number of guards required to see every point in an art gallery represented by a polygon with or without  ... 
arXiv:1702.03456v2 fatcat:k5kgkxm3rrgejcuomisguqpdca

On conflict-free chromatic guarding of simple polygons [article]

Onur Çağırıcı and Subir Kumar Ghosh and Petr Hliněný and Bodhayan Roy
2020 arXiv   pre-print
This is also known as the conflict-free chromatic guarding problem with vertex guards, and is motivated, e.g., by the problem of radio frequency assignment to sensors placed at the polygon vertices.  ...  We efficiently solve the related problem of minimising the number of guards and approximate (up to only an additive error) the number of colours required in the special case of polygons called funnels.  ...  Consequently, the guards placed at d 1 and d 2 must be of different colours (red and blue); otherwise, say for two red guards at d 1 , d 2 , each of the 8 vertices in A would have to be guarded by a blue  ... 
arXiv:1904.08624v3 fatcat:i5kh5en7src2zhdr7ulic5gcc4
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